Question re: Mooney M20J
 

What purpose does the NACA inlet on the fin fillet serve? Thanks

air vents
 

It supplies ram air to the 4 overhead eyeball vents. It's a seperate system to the vents near the pilot's knees that comes from the engine cowls. BE-76 Duchess has the same sort of thing.

Sorry I can’t help with a direct answer. The NACA inlet is a low drag means of obtaining outside air, probably just for cabin ventilation. A lot of design work was put into streamlining on this machine. I have always liked the Mooney, especially the M20J/M201. Unfortunately I never added it to my list of endorsements.
I did find this great reference http://www.answers.com/topic/mooney-m20
It has a concise summary of the many features of this little speedster.
Over many years in Control Towers watching Mooney pilots come and go it soon became obvious that controllers should watch out for something strange to happen especially on arrival. It seems that the slippery little things don’t want to slow down to circuit speed readily. It was always fun at PF on a busy day when a cross country visitor in a Mooney arrived!
The link above has a paragraph relating to the investigation done in the USA to try and determine why so many Mooney aircraft were involved in accidents.

Thanks, I thought that was what it was there for but I haven't flown one in over 10 years! A very nice efficient little plane they are too, just keep the prop out of the long grass...

Yep - great fun to fly once you get used to how slippery they are! Landing gear has about 1in of travel in it so a smooth landing can also be a real challenge.